Many transportation problems, such as the energy-efficient operation of electrical trains, guided transport systems at airports, or hybrid cars can be reduced to optimizing a velocity profile of a moving vehicle along a route. The velocity profile is called a run curve. If a distance along the route is denoted by z, then a desired velocity v(z) at position z describes the run curve. The run curve has to obey legal and mechanical constraints of the route, e.g. speed limits, safety margins, and must be physically realizable by mechanisms of the vehicle.
For example, an automatic train control (ATC) is a known method to control vehicles, such as trains. With ATC, when the velocity of the train exceeds a specified permitted maximum velocity over a particular section of the route, a brake system is activated and the train is decelerated. It is advantageous for the run curve determination to be adaptive to various constraints, such as constraints on the speed limit. For example, the velocity of the high speed train can be regulated according to a stepwise reduction of predetermined maximum velocities, i.e. 80 km/h, 65 km/h, 45 km/h, and 25 km/h. If the train is required to run at a given limited velocity over a certain section, then the permitted maximum velocity is gradually reduced in steps approaching a target limited velocity of the section.
However, the optimal run curve should provide more benefits that just obeying the legal constraints of the route. For example, in some situations, the optimal run curve should minimize running times between an origin and a destination, e.g., located at z=0 and z=Z, respectively. Additionally, the optimal run curve should minimize the required minimal energy consumed by the vehicle along the route.
Usually, these two requirements are contradictory to each other, i.e., the shorter the running time, the more energy is needed, and vice versa. Thus, there is a need to provide a method and a system for determining an optimal run curve for the vehicle.